A diatomic ideal gas initially at 273 K is given 100 cal heat due to which system did 210 J work. Th

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A diatomic ideal gas initially at 273 K is given 100 cal heat due to which system did 210 J work. The molar heat capacity of the gas for the process is (1 cal = 4.2 J)

Accepted Answer

$\Delta U = q + w = 100 + \left( - \frac{210}{45} \right) = 50\text{ cal = }n.C_{v,m}.\Delta T\text{ and }q = 100\text{ cal = }n.C_{m}.\Delta T$

$\therefore\frac{50}{100} = \frac{n.C_{v,m}.\Delta T}{n.C_{m}.\Delta T} \Rightarrow C_{m} = 2C_{v,m} = 2 \times \frac{5}{2}R = 5R$

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